時間がなくて

because I don't have time

→ 時間
phrase Rare #42,631
because I don't have time The て-form connects this reason to what follows.
JA: 時間がなくて、今日は行けません。
EN: I can't go today because I don't have time.

時間がなくて、最終バスに間に合わない。

I don't have enough time, so I won't make the last bus.

私は午後は時間がなくて行けません。

I don’t have time to go in the afternoon.

何しろ時間がなくてよ

I just don’t have any time.

— 天空の城ラピュタ (1986)

時間がなくてたいへん困っている。

I'm really struggling because I don't have enough time.