Bright, Adrian runs to the top, top of tower (7)

I believe the answer is:

radiant

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'bright' is the definition.
('radiant' can be similar in meaning to 'bright')

'adrian runs to the top top of tower' is the wordplay.
'runs' indicates anagramming the letters.
'to the top top of tower' becomes 't' (I can't explain this - if you can you should give a lot more credence to this answer).
'adrian' is an anagram of 'radian'.
'radian'+'t'='RADIANT'

Can you help me to learn more?

(Other definitions for radiant that I've seen before include "Bright" , "Lit up" , "beaming with joy" , "Luminous" , "Brilliant" .)

I've seen this clue in The Telegraph.

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