Admit learner inside a base (5)
I believe the answer is:
allow
'admit' is the definition.
(allowing is a kind of admiting)
'learner inside a base' is the wordplay.
'learner' becomes 'l'.
'inside' means one lot of letters goes inside another.
'base' becomes 'low' ('low' can be a synonym of 'base'**).
'a'+'low'='alow'
'l' going inside 'alow' is 'ALLOW'.
(Other definitions for allow that I've seen before include "Permit or agree" , "Grant" , "Permit or acknowledge" , "brook" , "Tolerate" .)