expression, i-adjective
not long has passed since ...; soon after ...
Used after the -te form of a verb to indicate that only a short time has elapsed since that action. Often implies that something else has already happened or is about to happen.
日本に来て間がないので、まだ日本語がよくわかりません。
It hasn't been long since I came to Japan, so I still don't understand Japanese well.
彼は卒業して間がないのに、もう結婚した。
He graduated not long ago, but he's already married.
間もなく is an adverb meaning 'soon' or 'before long', used for future events. 間がない is an adjective-like expression used after a verb to describe a short time having passed since that action.
From 間 (ma, 'interval, time') + が + ない (nai, 'not exist'). Literally 'there is no interval', used idiomatically to mean 'not long has passed'.