Admit Liberal is in a depression (5)
I believe the answer is:
Here is my best explanation:
'admit' is the definition.
(allowing is a kind of admiting)
'liberal is in a depression' is the wordplay.
'liberal' becomes 'l' (abbreviation).
'is in' means one lot of letters goes inside another.
'depression' becomes 'low' ('low' can be a synonym of 'depression'**).
'l' placed inside 'alow' is 'ALLOW'.
(Other definitions for allow that I've seen before include "Sanction", "Permit or acknowledge", "Let", "Own", "Give leave to", "Acknowledge - concede", "Permit or concede", "Permit, let happen", "OK" and "grant".)