。
I'll take over your work.
Literal
I [subject-が] your work [object-を] take-over-[volitional-う].
引き継ぐ ('to take over, to inherit, to succeed to') is a compound verb — 引く ('pull') + 継ぐ ('inherit, continue'). Used for inheriting responsibilities, roles, traditions. The volitional 引き継ごう signals the speaker's proposal or promise to undertake the takeover.