Writing to doctors, healers around America with time to practice in the theatre (9)
I believe the answer is:
rehearsal
'time to practice in the theatre' is the definition.
I can't judge whether this defines the answer.
'writing to doctors healers around america' is the wordplay.
'writing' becomes 'rehears' (I can't explain this - if you can you should believe this answer much more).
'to doctors' indicates an anagram.
'around' says to take the centre.
'america' becomes 'a' (common abbreviation - e.g. in organisation names).
The middle of 'healers' is 'l'.
'l'+'a'='la'
'la' anagrammed gives 'al'.
'rehears'+'al'='REHEARSAL'
'with' is the link.
Can you help me to learn more?
(Other definitions for rehearsal that I've seen before include "Practice session in preparation for public performance" , "Drill" , "Dummy run" , "Preparation for a show" , "Dry run" .)