Check out Texan's unlimited oil source (7)
I believe the answer is:
examine
'check out' is the definition.
(to examine something is to check or test it)
'texan's unlimited oil source' is the wordplay.
'unlimited' means to look at the middle letters (remove the limits/outer letters).
'oil source' becomes 'mine' (I am not sure about this - if you are sure you should believe this answer much more).
The middle letters of 'texan' are 'exa'.
'exa'+'mine'='EXAMINE'
Can you help me to learn more?
(Other definitions for examine that I've seen before include "Test, probe" , "vet" , "Subject to inspection" , "Question (a witness)" , "Question closely" .)