Throat condition that is beginning to restrict dealer (8)
I believe the answer is:
croupier
'dealer' is the definition.
(similar to a dealer in a casino)
'throat condition that is beginning to restrict' is the wordplay.
'throat condition' becomes 'croup' (throat inflammation affecting children).
'that is' becomes 'i.e.' (synonyms).
'beginning to' says to take the initial letters.
The initial letter of 'restrict' is 'r'.
'croup'+'ie'+'r'='CROUPIER'
(Other definitions for croupier that I've seen before include "Person in charge of gambling-table" , "Casino attendant" , "I procure from person in charge of gambling table" , "Leisure worker" , "rakes in the money" .)