Beginning to regret filling pink pen (6)
I believe the answer is:
corral
'pen' is the definition.
(both are a type of enclosure for animals)
'beginning to regret filling pink' is the wordplay.
'beginning to' indicates taking the first letters.
'filling' indicates putting letters inside.
'pink' becomes 'coral' (coral is a shade of pink).
The initial letter of 'regret' is 'r'.
'r' inserted inside 'coral' is 'CORRAL'.
(Other definitions for corral that I've seen before include "Western horse enclosure" , "Pen for livestock (US)" , "Livestock enclosure" , "Pen for cattle in the US" , "Pen for cattle - ring of waggons" .)