Where does “затаивать” come from?

затаивать (Russian) comes from Russian затаи́ть, from Russian за́-, from Proto-Slavic za- — for.

Ancestry of “затаивать”, step by step

Step	Language	Word	Meaning
1	Russian	затаи́ть	—
2	Russian	за́-	—
3	Proto-Slavic	za-	for

затаивать — Etymology, Origin & Word History | Etymology Explorer