It looks like metal?Oh my Hi-Tech fix
Plumbers tape, a drill, and wood/plastic screw. Fortunately I had the original plastic piece that broke so I was able to emulate the same shape.
22 gauge Plumbers tape works great because it's flexible yet will not "crack" so it will apply enough pressure when sliding turn signal light back in and resume it's shape.
If you don't have the original piece, you'll have to trial and error the shape size but you can use my pic as a guide.
1. Drill a small hole thru plastic clip base (match hole size to screw you plan to use)
2. Cut and shape Plumbers tape to match "normal" clip
3. Attach shaped plumbers tape with plastic/wood screw
4. Make sure the plumbers tape clam contact point is rounded or else it will snag
I was thinking of doing a spring loaded setup, but that would have just been way too nerdy so I opt'd for the simple ghetto yet functional and durable solution.
FYI, my turn signals just popped out one day while washing the car, they don't need to be removed when the front clam is remove -- I just decided to fix the problem since I was fixing other issues.