In the southeast, where part of a lake is National Trust (4)
I believe the answer is:
kent
'where part of a lake is national trust' is the definition.
The answer is a location as well as being a singular noun. This is suggested by the definition.
'in the southeast' is the wordplay.
I cannot quite see how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found in the answer.
The remaining letters 'ken' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for kent that I've seen before include "County of SE England" , "known to Scots" , "County, garden of England" , "South-eastern county" , "Garden of England - Superman's family name" .)