Clara Oswald is well aware of the phenomenon commonly known as pangs of jealousy.
They're not a far-fetched possibility around this man she tends to be around of.
She obviously knew of Professor Song and his other marriages, she kept tabs on his offhanded mentions and anecdotes to puzzle together images of everything from rather random unscheduled lip-collisions, to brief love affairs that were often tragically cut short or constrained by impossible circumstances, to specific names he'd sometimes mention, the "Sarah"s, "Peri"s and "Romana"s he'd speak of with fond respect or the "Jo", "Charley" and "Rose" that would sometimes tinge his voice and face with varying degrees of yearning wistfulness.
It didn't take much imagination to speculate that some of them might have reacted with a bit of jealousy, it was only human, after all. Others perhaps, were themselves people that did not like to be tied down in any way and thus, didn't expect it of him, either.
Where did Clara fall on that scale? Well, she was 'human' as well, but she was supposed to be a mature person. She never expected to have been the first one to have traveled with him, and understood that there had been a long before, and that there would be a long after; She hoped so, at least, given that the alternatives would be outliving him or leaving him to a miserable future. There was also that little factoid that she wasn't officially supposed to be anything of his, as flimsy as the denial had once gotten in places and, at times, still got, and even if she was, she could understand that there was obviously a time before he'd met (or become aware) her, (even if they could make it their "now" rather easily thanks to their nifty time machine), and back then, he'd be quite free to do things like marry the (then) queen of England (and get snogged senseless by her), she'd even be his maid of honor and throw some glitter for the occasion! ...but a point would come at which her smile would crack, her emotions would force their way past her rational mind and she'd wind up rolling her eyes... or skip to the eyes-rolling right away if he situation was surreal enough which, with him, it often was.
To be frank, she would not pretend that she, in any way, enjoyed to see him kiss other people, or even having to hear that he had a granddaughter, and thus, at some point, spawned at last two generations of offspring with someone who wasn't her.
She could not guarantee that what was true in quiet moments would hold true in the heat of a moment, but when she was at her desk doing work or contemplating the day sitting on her bed, when she could think things through completely and , she could, at least on an abstract, intellectual level, say that she was fine with Professor Song, Elizabeth, Tasha. If they were parts of his story, if they had helped him on his long path and kept him in one piece so he could even get to her, if they were part of the reason he was how he was, then she was grateful towards this Rose, Charley or Romana, even the Master, as much as Clara despised that evil creature in the end.
And him?
Well, it was not in any way correct to call him a jealous person. He wasn't the type to resent others for their happiness, or dismiss and devalue something because it didn't match his personal taste, wasn't suited to him, or simply something he couldn't have; (although it could be hard to tell nowadays... and actually, before, too, with the way he'd sometimes belittle everything in sight when he was sufficiently bored or frustrated) If someone he cared about was happy, especially if he could still contribute to giving them happiness, then he was able to do what many took for granted when it was the pain or someone they loved, and share it as if it were his own, to, in a sense, live vicariously through them.
Despite, or maybe in part because of what his vanity and general haughtiness about his intellect may suggest, he didn't really have that high an opinion of themselves and odds are, if he'd talked to a person long enough to be seriously interested in them, he'd already have a complex bundle of guilt about supposedly ruining their lives, regardless of whether his actual impact on their lives under account of the circumstances was actually negative, positive or overall... mixed.
Then, there was the matter of his age – given that Time Lords were simply a relatively long-lived species, it was more or less unavoidable that nearly anyone he came across would be vastly younger than himself; (Then, of course, there had been Romana, with whom there had still been a significant disparity in age and experience, if, to his embarrassment, not in engineering skills) Other Time Lords had been somewhat unavailable as of late, and even back when they weren't, that stagnant society with its largely stuffy, detached and condescending people were something he'd run away from, and never felt the slightest bit inclined to return to.
It has to be said that sometimes, the best indicator of who someone is and what is important to them is not where they come from and the people they got stuck with, but the people they chose to surround themselves with, those who caught their attention, the ones that evoked empathy, sympathy or admiration in them.
Even if he didn't have that particular fondness for their home world, after certain points in time, humanity was simply spread out all over the universe, and one was likely to encounter them wherever they went. So if he went out there and met people, some of which then manage to impress him, chances are that some of them will be human either way; While he had his fair share of Alzarians, Trakenites and tin dogs tagging along and was always open to all forms of life, as it stood, most of his friends were human, what he'd call co-workers or comrades, much of what he'd come to consider his family and, in the end, probably shared more in common with that with most of his actual blood relatives... So it should not have been surprising that most of his lovers had been human as well, simply because most of the people around him were.
Both the species and age differences were just something he'd have to deal with as a consequence of the life he led –
but it certainly contributed to the way he was always very quick to give them up for the sake of their happiness, more so than even selflessness could justify.
Still, there were always circumstances that made it easier than others.
If he really liked suitor option B, if he was courageous, dependable and willing to compromise, everything she needed and what he himself wished he could be, and, just to top it off, the happy couple made it clear that they still wanted him in their lives as their friend, champion, or even a part of their family, well, perfect! Time would just let the inconvenient feelings dissipate on both sides dissipate, he'd come to care in a different capacity, concern himself with giving them happiness, and find someone else for... the other stuff, and it all works out fine for everyone involved.
Another sort of comfort or consolation prize that... at least allowed him to exit the stage with his ego intact, or his comfortable illusions, should he feel the need to indulge in them in some lonely, pitiful moment. A lookalike, a promising young activist explicitly described as a younger version of him, a suspiciously loud-and-brusque-yet-heroic warrior king, an actual duplicate... he could deal with that, he could deal, and still tell the portions of himself that were childish enough to think in such terms that he'd still "won", or could have, or at least had a confirmation that she'd... liked him, too. He could deal. The flip side of that coin was a sharp pain that twisted the knife further, a sense of betrayal he had no business feeling, distraught over losing a chance that might have been real, yet hurt that the other person would chose an 'easier' suitor, basically similar but without all those confusing, edgy alien bits to deal with, even when that was exactly what he'd wanted to give them, even personally orchestrated... and that, too, just affirmed his belief that he was right to leave.
But one shouldn't need an 'ego boost' to cope with doing-the-obviously-right-thing to begin with. And maybe a better, more honest person wouldn't.
There was, however, a difference between choosing to do what he probably should, and being able to turn off one's feelings with a button; He was rather like Clara in that respect, although she'd probably like to contest that, given that his own encounters with the green eyed beast tended to be amazingly more blatant, to the point that they were moderately annoying rather than flattering.
He did only slightly mind when she got cozy with any of the locals of a place they were going to leave soon anyway, or heard her mention going on dates in-between trips, although he was not exactly beneath a little playful sabotage, but that was because he was an arrogant jackass and didn't see any of this as a 'serious threat'.
Anyone who legitimately drew her attention away from him was another story.
Oh sure, he might make a token effort to play nice, but when he found a pretext not to hold back, ("Must be a robot!") she would wind up practically smelling the testosterone, or whatever the Time Lord equivalent of that delightful little chemical happened to be.
Even when he was perfectly willing to bow out gracefully, it took a conscious effort to dial down the smartass and stop competing. Part of it was probably just being a showoff by nature, for its own sake, before impressing anyone specific even came into the picture.
Something he also was: Desperate, at times. Like when he did not want to lose the first speckle of thorough happiness he had grasped after the Time War, or whenever he was around Clara, because he was always desperate when it came to her, more than he would, or even could ever show.
She was the person who brought out that side in him, the heated and passionate bordering on obsession – Because she is the one who had witnessed his secrets and seen him as he really was, at first, through accident and necessity, later, because he trusted her, then, because he wanted her to know. For the first time in his long life, he not only trusted, but wanted someone to know exactly who he really was, wanted her to see him, only him, all of him, from his unpolished surface to his rotten core.
She had stayed at his side to support him, through the days of boon and the lean times, and while she did struggle with him, she never left his side for long. She was the existence that appeared before him in his days of doubt and darkness, and each time, she had her way to stir the embers of all that was still alive inside of him, and this was why he kept wanting her all for himself, wanting all of her, always, endlessly wanting even long after he had given up.