Cheer that woman catching a number (7)
I believe the answer is:
hearten
'cheer' is the definition.
('hearten' can be a synonym of 'cheer')
'woman catching a number' is the wordplay.
'woman' becomes 'her' (**).
'catching' is an insertion indicator.
'number' becomes 'ten' (ten is a kind of number).
'her' placed around 'a' is 'hear'.
'hear'+'ten'='HEARTEN'
'that' is the link.
(Other definitions for hearten that I've seen before include "giving cheer" , "Make (someone) more confident" , "Make cheerful" , "Encourage in Teheran" , "Encourage or cheer in cardiac manner" .)