Synonyms for take-up

Most common

1. Absorb

2. Latch onto

latch onto, latch on, seize on

Other

lift, raise, discharge, settle, resume

v. 1
To lift; to raise. To pick up.
v. 2
To lift; to raise. To remove (a ground or floor surface, including the bed of a road or the track of a railway).
We're going to have to take up the floorboards.
n. 1
The act of taking something up, by tightening, absorption, or reeling in.

4 letters: take¹, draw¹, fill¹, lift¹, suck¹, sorb
5 letters: start¹, cover², catch¹, raise¹, begin², adopt², scoop¹
6 letters: strike¹, assume², arrest², engage², settle², resume², employ², borrow², occupy³, absorb²
9 letters: discharge²

The small number after each word is its number of syllables (cover² = 2 syllables).