Video material of New Musik is pretty scarce. I'll mention here what I am aware of but I'm sure there's more hence please contact me with other material you find.
Most notable for NM fans is the Listen To London DVD. Released in 2008, it is a "fly on the wall" docu-video charting the 1981 London post-punk indie scene. New Musik are featured for a healthy 8 minutes, with live footage featuring 'Straight Lines' in its entirety plus snippets of 'Living By Numbers' and 'World of Water'. There is also a short interview with Tony Mansfield and Clive Gates. All in all this is absolute gold-dust for New Musik fans.
Here's a shot taken from the DVD, lots more in the band gallery...
OK, the other material can be found on - you guessed it - Youtube. By its very nature, Youtube is a "moving feast" and new stuff can appear as fast as existing stuff disappears. Hence, these links were working "at the time of going to press" so-to-speak. :-)
Het Vierde New Pop festival (1980) Rare live footage from a pop festival in Rotterdam.
Living By Numbers Studio promo vid (thankfully bereft of Steve Wright's sarcastic and unfunny comments from TOTP2).
Straight Lines (TOTP) Rare TOTP appearance from 1979.
This World of Water (Video) The promotional video.
This World of Water (TV) Rare appearance on Dutch TV.
There are numerous personal DIY tributes to various New Musik tracks also available on Youtube. Simply do a search.
Also there are various Tony Mansfield related videos on Youtube, a brief selection follows:
Aha / Take On Me (Tony Mansfield Mix) The original mix by Tony.