It takes a high place in the study of geometry (4)
I believe the answer is:
apex
'study of geometry' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'it takes a high place in the' is the wordplay.
'it' becomes 'e' ('e' can mean 'electronic' which is similar to 'IT').
'takes' means one lot of letters goes inside another (take can mean to capture or invade).
'high' suggests taking the first letters (I've seen 'highest of' mean this (top letter - down clues only)).
'in the' becomes 'x' (I can't justify this - if you can you should believe this answer much more).
The first letter of 'place' is 'p'.
'a'+'p'+'x'='apx'
'e' going within 'apx' is 'APEX'.
Can you help me to learn more?
(Other definitions for apex that I've seen before include "The highest point of something" , "Tip -- top" , "Peak, vertex" , "Summit - pinnacle" , "Topmost point" .)