Tropical tree sheltering English king twice in battle (9)

I believe the answer is:

naseberry

I'm a little stuck... Click here to teach me more about this clue!

'tropical tree' is the definition.
'naseberry' can be an answer for 'tree' (I've seen this before). I'm not sure about the 'tropical' bit.

'sheltering english king twice in battle' is the wordplay.
'sheltering' is an insertion indicator.
'english' becomes 'E' (abbreviation).
'king' becomes 'R' (abbreviation for rex, king in Latin).
'twice' indicates the doubling of some letters.
'in battle' becomes 'naseby' (Naseby is an example. I am not sure about the 'in' bit.).
'r' doubled is 'rr'.
'e'+'rr'='err'
'err' put within 'naseby' is 'NASEBERRY'.

Can you help me to learn more?

(Another definition for naseberry that I've seen is " Tree".)

I've seen this clue in The Times.

Want a hint initially instead of a full solution? Install my app