This is the 823rd most frequent Korean word.
있었지만
"있었지만" means "there was/were, but" or "had, but."
Here, '있었지만' conveys availability of time earlier in the day that contrasts with the current lack thereof.
아침에는 시간이 있었지만 지금은 바빠요.
I had time in the morning, but now I'm busy.
'있었지만' expresses the occurrence of a positive experience in the past, which does not influence the present preference.
그 식당에서 좋은 경험이 있었지만 다시 가고 싶지는 않아요.
I had a good experience at that restaurant, but I don't want to go again.
In this sentence, '있었지만' is used to indicate the past existence of a commitment that nevertheless could not be fulfilled.