2636: Happy ever after

Twelve unclued lights may be grouped into three quartets and their unchecked letters spell out ask engineering-academy.gov.uk; each quartet comprises two natural pairs. All unclued entries are normal words, one is in Merriam–Webster and one is thematically linked to its quartet via a Broadway musical.

Across

1   Maybe PC speed unit cut after unexpectedly taking van (8)

6   About to display ancient nut (6)

12   Local scolding somehow raises your back (8)

13   Developer of global movement almost left (5)

14   Dogged has-been hooligan welcomes trouble (6)

15   Chain two blokes side by side (6)

20   Returning from Dubai, unnerving bore (5)

21   American people embracing setter’s vigour (9)

24   Extremely sick and unwell, dispersing in Glasgow? (8)

25   Obduracy shown by most of gang outside North London? (8)

30   Zigzags in descent at swimming (9)

31   William (Bill) covers at least two feet (5)

35   European industrial gear grabs earth, perhaps (6)

36   Joyous cry from house, talk-show host belting out piano (6)

37   Character on staff, ultimately retiring, all but split (1,4)

38   Spiders managed to perish, rolling in lava (8)

41   Rancid point, between the lines (6)

42   Snare docked dog crossing lake (8)