I am looking for information regarding an Organist or Pianist named C.
Jarvis that lived in London around 1800 - 1830 and was a Pupil of a
famous musicist named William Gardener. He used to work for some Clock
Makers of his time composing music for musical clocks (roll with
pins). He did that at least for one Clock maker of Clernwell Close,
London, called Handley and Moore.

At first, I suspected that Charles W. Jarvis (1809-1871), a British
composer who emigrated to the USA in about 1835, could be the right
one ... but then I found out that at least one clock "C. Jarvis"
arranged the music for is dated 1818. And since it is highly unlikely
that Mr. Jarvis was an arranger already at the remarkable age of 9, I
dropped this idea again...

http://www.converseclocks.com/inventory.asp?m=i&k=271

Maybe one of my colleagues finds the correct path in this case...

Scriptor

Some biographical notes on William Gardiner (1769-1853):

http://www.cyberhymnal.org/bio/g/a/gardiner_w.htm

http://www.canamus.org/Enchiridion/Biogs/bg1.htm

http://www.blc.edu/comm/gargy/gargy1/ELH.biographies.EFGH.html

However, Jarvis not mentioned.

"... Miss Jarvis ... " " ... taking part in the concert, which had
been organised by William Gardiner ..."

http://www.leicesterresearch.co.uk/page09n.htm

Could Miss Jarvis be the person you are looking for?

The webmaster of 
http://www.leicesterresearch.co.uk/
may have some additional information or could give you some clues how
to proceed with your research.

The bicentenary sketch "William Gardiner of Leicester (1770-1853)"
written by Jonathan Wilshere and published in 1970 is still available
http://www.indigogroup.co.uk/albion/wilshere.htm

In this booklet (35 pages) you may find some information on Jarvis.