Look fixedly on old boy going round summerhouse (6)
I believe the answer is:
gazebo
'summerhouse' is the definition.
(synonyms)
'look fixedly on old boy going round' is the wordplay.
'look fixedly' becomes 'gaze' (I've seen this in another clue).
'on' says to put letters next to each other (in a down clue, letters appear on others).
'old boy' becomes 'OB' (abbreviation for a private school 'old boy').
'going round' says the letters should be written backwards.
'ob' back-to-front is 'bo'.
'gaze'+'bo'='GAZEBO'
(Other definitions for gazebo that I've seen before include "Raised summerhouse with a wide view" , "Summerhouse - pavilion with view" , "Small garden house with a view" , "outhouse" , "Type of summerhouse" .)