Well, you know what they say about assuming things…
But seriously, unless otherwise stated, it would be much more likely that the earlier binds the former, just as legal precedent itself means that older decisions are binding on future decisions. In this case, my contention is that, having sworn the oath of knighthood, Jaime is not in fact completely free to swear to “Defend the king. Obey the king. Keep his secrets. Do his bidding. Your life for his” in any situation where obeying the king or doing his bidding would cause him to violate the first oath.
To take an example that’s not too farfetched given events in ASOIAF: given that the oath of knighthood requires knights to “protect all women” and to “defend the young and innocent” should a kingsguard obey Joffrey’s command to beat Sansa? I would argue that Sansa’s ACOK chapters suggest strongly that any knight who obeys such a command is not a true knight, whether we’re talking about brutes like Boros Blount or Meryn Trant or the squeamish like Arys Oakheart.