Cryptic crossword No 3,701

Across

1. Brave victor pursued by the greatest soldier (7)
2. Countries in agreement behold heartless guy giving speech of late (6)
3. The Offspring's issue with piano: sharp when left transposed to D (10)
4. Way to ultimately become Republican and bellow (4)
5. Rushes nothing small (4)
6. Alum bent out of shape about ace that's wild (9)
7. Comedian's staff beginning to borrow most of additional equipment for Countdown (3,8)
8. Comic almost curiously breaking down inside (9)
9. Wheel made of hard wood (4)
10. Nothing grand about monster (4)
11. Braggart son, a so-called revolutionary, incorporates family business? (4,6)
12. Saying papers backtracked about corporation (6)
13. Side pieces cease regularly leaving puzzling fellow? (7)

Down

1. Label on unwrapped prize carpet (6)
2. Short kid regularly found lint in dryer (4)
3. Second-degree criminal act: raid queen beforehand (9)
4. Day in Paris ending in fifteen beers primarily energises reporter's writing (10)
5. Make out lawyer with English name standing up (4)
6. Annual club meeting ahead of schedule (6)
7. Wife that is at unrest, madly eating casing of raw sausage (11)
8. Public relations with poet in Rome, and subsequently decapitated -- that's destiny (10)
9. Am I overwhelmed by a Frenchman's thanks? Um... (9)
10. Evaded rabbit hunter trapping first couple of geese (6)
11. Crows about drumrolls? (6)
12. God in time at crux of deism (4)
13. That woman would get rid of storage unit (4)