Production of Lear outside picks up in run-through (9)
I believe the answer is:
rehearsal
'run-through' is the definition.
(I've seen this before)
'production of lear outside picks up' is the wordplay.
'production of' indicates anagramming the letters.
'outside' is an insertion indicator.
'picks up' becomes 'hears' (hearing is a kind of picking up).
'lear' with letters rearranged gives 'real'.
'real' enclosing 'hears' is 'REHEARSAL'.
'in' is the link.
(Other definitions for rehearsal that I've seen before include "Dramatic practice" , "Preparation for a show" , "Dry run" , "preparation in house?" , "Drill" .)