In general English one might distinguish between:
in time: rechtzeitig
on time: pünktlich
If you arrange to record a TV programme at 9.00 a.m., you want to start recording on time – on the dot of nine.
If you have to do something by / before December 31, you need to do it in time – before the final date.
(I bought a jar which had the wording ‘Eat the contents until December 2014’ instead of ‘Eat the contents before December 2014’)
In legal texts, there are often deadlines, and the word rechtzeitig comes up for translation, both as an adverb and as an adjective.
In BrE I would say: in good time or within the prescribed period.
One also encounters, in AmE but also in BrE: in a timely manner. (timely is an adjective, not an adverb)
I’ve just been reminded of a word that works better grammatically if you need an adverb: timeously.
Laddie J … said that, at the end of the opposition period and in the absence of opposition, the Registrar was obliged to take steps timeously to place the mark on the register.
There’s a complex of further vocabulary here, for German Frist: a period of time but also a time limit / deadline. I believe deadline is regarded as more AmE usage, but I see no problem with using it. It’s probably more common in general usage than legal texts, though.