Match official's hesitation about booking Greek character (6)
I believe the answer is:
umpire
'match official's' is the definition.
'umpire' can be an answer for 'official's' (umpire is a kind of official). I'm not sure about the 'match' bit.
'hesitation about booking greek character' is the wordplay.
I cannot really see how this works, but
'hesitation' could be 'um' (sound made when hesitating) and 'um' is located in the answer.
'about' could be 're' (regarding) and 're' is present in the answer.
'character' could be 'pi' (pi is a kind of character) and 'pi' is located in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for umpire that I've seen before include "A field judge in circket" , "Person enforcing rules" , "One enforcing the rules in games" , "Adjudicator in games such as cricket, tennis etc" , "Game judge" .)