At Beachy Head, there's much that's an eyesore! (4)
I believe the answer is:
blot
'an eyesore' is the definition.
(I've seen this in another clue)
'at beachy head there's much' is the wordplay.
'at' means one lot of letters go next to another.
'head' suggests taking the first letters.
'there's much' becomes 'lot' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The initial letter of 'beachy' is 'b'.
'b' next to 'lot' is 'BLOT'.
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for blot that I've seen before include "Ink stain; disgrace" , "Spot of ink, paint etc" , "bad mark" , "Cross out; inky mess" , "Ink mark" .)