Can I use Shimano Claris shifter to my Shimano Tourney road bike
No. The sprocket spacing gets narrower as the number of sprockets goes up - to keep the cassette width constant (until 11 speed where it gets slightly wider).

An 8 speed shifter will not index correctly as it is pulling cable length increments for 8 speed spacing not 7 speed. 

Tourney isn't really compatible with any Shimano components in the levels above it, so a better route to go would be to replace the entire groupset (you can probably get away with not upgrading the crank). 

Many people in this community feel that Tourney level bikes are not worth spending money on upgrading, and it's better to sell them and buy a whole new bike a step up.