Is it possible to develope shields like in star-trek??

its possible but would be very hard to do i am no expert on that topic i do know you can have a force that pushes things away a strong force shield around something but if such a thing could be made to stop missiles that seems to be far away technology. They are now just getting FEL down and trying to put them on ships and use them for missile defense that will take probably 10-15 years until they are operational.

You could theoretically use magnatism and hot plasma to build a shield around a spacecraft. The plasma could dispearse lasers and melt projectiles, missles etc... it would not shield against everything though. You would still want a thick hull plate and possible some other technology under the sheild to catch anything that makes it through the plasma.