You could, depending on the amount and application, use StageTips or ZipTips with C18 column material. After binding the peptide to the resin wash with 5% formic acid, transfer the tip to a clean tube, and elite with 0,1% formic acid in 80% acetonitrile and dry the sample in a freeze-dried or speedvac.

I used to do it in 2 steps. After centrifuging the sample to pellet the precipitate, I removed nearly all the supernatant by gentle suction, being careful to avoid disturbing the pellet. Then I would spin the samples again and remove the residual supernatant with very gentle suction using a Pasteur pipette drawn out in a flame into a fine tip. This procedure lets you remove all of the supernatant without endangering the pellet.

If your pellet is big, some TCA could remain in your sample, and consequently it will interfere in electrophoresis for instance.

I used to wash the pellet at least twice with acetone after TCA precipitation.

All the best!

In addition to Adam's and Rosa Maria's suggestions, I would shake the (dried) pellet with chilled diethyl ether a couple of times. Just make sure that your centrifuge is compatible with ether, and that the ether is fresh and peroxide free. Ethyl acetate is another alternative. Acetone may form adducts with your peptide, and even though that is reversible, it is generally best to avoid.

If traces of TCA still remain, then evaporate any residual organic solvent under a stream of nitrogen before proceeding to C18 purification as described by Simon.

You can do a combination of TCA precipitation followed by Acetone washing of the pellet or do a dialysis against an appropriated buffer and with a pore cut-off lower than the size of your protein.