This will leave only the update version number:
echo "1.0.0-1" | sed -e 's/^[1-9][0-9.]*-//'
And this will leave the leading '-' on it:
echo "1.0.0-1" | sed -e 's/^[1-9][0-9.]*//'
The p command isn't needed in the above so I left it, and the -n option off, but you can restore them if this part of some more elaborate sed script.
Edit: OP apparently just wants to know if the version contains an update. Here are a couple of ways in classic bourne shell:
#!/bin/sh
version='1.0.0-1'
case "$version" in
*-[1-9]*) # Not a regex, this is a (file) "pattern"
# Update triggered code here
;;
esac
# Or:
if echo "$version" | grep '-[1-9][0-9]*$' >/dev/null ; then
# Update triggered code here
fi
There are other ways to do it in other shells/environments of course.