Artisan beginning to get more lethargic (7)
I believe the answer is:
glazier
'artisan' is the definition.
(glazier is a kind of artisan)
'beginning to get more lethargic' is the wordplay.
'beginning to' indicates taking the first letters.
'more lethargic' becomes 'lazier'.
The first letter of 'get' is 'g'.
'g'+'lazier'='GLAZIER'
(Other definitions for glazier that I've seen before include "Person who cuts flat glass to size" , "Craftsman" , "Skilled worker" , "Window mender" , "One may fix lights" .)