When a roof is installed the drip edge should be installed during the roofing process.
But some residential roofs don't have any drip edges installed on existing roofs because although it helps to protect the roof it's not always necessary.
But yes if you want to install a drip edge on an existing roof you can do so by gently lifting up the shingles and sliding the drip edge under it and if you cannot nail it down then you possibly use some type of glue to hold the drip edge down.