Had a meal in South Dakota, becoming full (5)
I believe the answer is:
sated
'full' is the definition.
(I've seen this in another clue)
'had a meal in south dakota' is the wordplay.
'had a meal' becomes 'ate' (ate a meal).
'in' indicates putting letters inside.
'south dakota' becomes 'sd' (abbreviation).
'ate' going into 'sd' is 'SATED'.
'becoming' acts as a link.
(Other definitions for sated that I've seen before include "fully filled" , "Stuffed with food, too full" , "Stuffed, having had a surfeit" , "completely filled?" , "Glutted" .)