Classy types away in borders of Texas (5)
I believe the answer is:
toffs
'classy types' is the definition.
(upper-class types)
'away in borders of texas' is the wordplay.
'away' becomes 'off' (synonyms).
'in' means one lot of letters goes inside another.
'borders of' means to remove the middle letters.
'texas' with its middle removed is 'ts'.
'off' inserted inside 'ts' is 'TOFFS'.
(Other definitions for toffs that I've seen before include "smart people" , "Posh blokes" , "Posh people" , "aristos" , "Posh folk" .)