Art collector in midst of assessing properties (7)
I believe the answer is:
Here is my best explanation:
'properties' is the definition.
(estate is a kind of property)
'art collector in midst of assessing' is the subsidiary indication.
'art collector' becomes 'tate' (UK institution organising four art museums).
'in' means one lot of letters goes inside another.
'midst of' says to take the centre.
The centre of 'assessing' is 'ess'.
'tate' put into 'ess' is 'estates'.
(Other definitions for estates that I've seen before include "Properties", "Large cars", "residential areas", "Extensive landed properties", "Property?", "Lands", "Landed properties", "Demesnes", "Country properties" and "Cars with rear doors".)