Serious four score at shallow end (7)
I believe the answer is:
weighty
'serious' is the definition.
('weighty' can be a synonym of 'serious')
'four score at shallow end' is the wordplay.
'four score' becomes 'eighty' (I've seen this before).
'at' means one lot of letters go next to another (I've seen this in other clues).
'end' says to take the final letters.
The final letter of 'shallow' is 'w'.
'eighty' put after 'w' is 'WEIGHTY'.
(Other definitions for weighty that I've seen before include "Important" , "Heavy - very serious" , "substantial" , "Cumbersome" , "having great influence" .)