Thinking Reg must keep a son at home (9)
I believe the answer is:
reasoning
'thinking' is the definition.
(reasoning is a kind of thinking)
'reg must keep a son at home' is the wordplay.
'must keep' means one lot of letters goes inside another.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'a'+'son'+'in'='asonin'
'reg' enclosing 'asonin' is 'REASONING'.
(Other definitions for reasoning that I've seen before include "Train of thought" , "Thinking that is coherent and logical" , "Logic" , "argument" , "Thinking coherently and logically" .)