Clues:

Across
1. Writer brandishes extended weapon (11)
7. Racehorse sounds audibly like a non-starter (5)
9. Married male though muddled makes theorem (5)
10. Pilfered church garment (5)
11. Beaten cadet must hurt to meet expectation (3,3,7)
14. Good lass, it’s clear (5)
18. Bestow open window (5)
19. Offspring is female (5)
20. Destroy old flame with fire (11)

Down
1. Dynasty is primarily sort of noble genealogy (4)
2. Boxer cut allowance for smaller portion (7)
3. Resonant energy transmitted over radio (4)
4. Copies found in antiparallel escalators (7)
5. Trees have the Spanish degenerative disease (4)
6. Held up, the engine’s gone! (7)
8. German is sounding hesitant over exploitations of strips of land (9)
11. Trim a piece of metal over cold water (7)
12. Partly clever, mostly stupid (7)
13. Masters home in summery area (7)
15. Wait for new deli (4)
16. Small, artlessly made martini (4)
17. Fellow comes in 4 types (4)

Solutions:

Across
1. Shakespeare
7. Neigh
9. Lemma
10. Stole
11. Cut the mustard
14. Glass
18. Indow
19. Issue
20. Exterminate

Down
1. Song
2. Aliquot
3. Echo
4. Alleles
5. Elms
6. Stalled
8. Isthmuses
11. Coppice
12. Halfwit
13. Augusta
15. Idle
16. Mini
17. Gene