Takes further education: keeps including basic element thereof? (8)

I believe the answer is:
retrains
'thereof?' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.
'takes further education keeps including basic element' is the wordplay.
I cannot really see how this works, but
'takes' could be 'trains' ('train' can be a synonym of 'take') and 'trains' is located in the answer.
'element' could be 're' (Re is an example) and 're' is found within the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for retrains that I've seen before include "Repeats a course of instruction" , "Learns new skills" .)
