First thing - don't rush to call a repair person. Often the problem can be solved with simple checks you can do yourself. Check if the drain filter is clogged (usually it's at the bottom front of the machine) - that's where hair, threads, and small debris accumulate, and they can prevent water from draining properly before the spin cycle. Also inspect the drain hose for kinks or blockages - sometimes the machine starts the spin cycle, but water doesn't completely drain from the drum, so the laundry stays wet.
Second thing - check if you're loading the drum correctly. If there's too much stuff or it's packed too tightly, the spin cycle might not work effectively. Try washing smaller loads at a time and see if that changes things. Also make sure you're using the right cycle: sometimes people habitually pick delicate cycles with low spin speeds, and the clothes naturally stay more damp.
If nothing changes after these checks, then yes, you'll need a repair person. Most likely the problem will be with the pump (drain pump) - it can lose power over time, or the sensor that controls the water level. But definitely check the filter and hose first - that often does the trick.