The unclued lights, (one individually, one of two words and three pairs), are of a kind.
 

Across

 
4    Popular executive having brush with copper can’t be condoned (11)
12    Left back’s round, round body (5)
13    Artless pastor immersed in revenue probe (11)
14    It’s steady to be unsteady (4)
15    One member’s a scoundrel (3)
18    Remained firm to the finish and awfully rude (7)
19    Levantine query to god’s high priesthood (7)
23    Returning runner has cost of Malay fabrics (6)
24    1300H — united — agree? (5)
27    Wild dog’s pain once spoken of (5)
29    Active seaman...