One who’ll stage a play and record it when running (8)
I believe the answer is:
director
'one who'll stage a play' is the definition.
'record it when running' is the wordplay.
'when running' is an anagram indicator.
'record'+'it'='recordit'
'recordit' is an anagram of 'DIRECTOR'.
'and' is the link.
(Other definitions for director that I've seen before include "This person could be on board or in theatre" , "Company board member" , "Creditor (anag.)" , "He makes films or runs companies" , "Senior person in a firm, executive or non-executive" .)