How do I repair cracked grout?

I have white grout in a downstairs shower wher it has a small crack right the way from floor to ceiling in the grout itself, not the tiles.

What is the best way of repairing it as I would assume water can get in behind it, although it's a concrete wall downstairs.

Should I just grout over it again to fill the gap or try to pull it out and redo it?

You could rake out the grout and re seal with fresh fine grout or get waterproof caulk and fill the crack.

I would run a bead of silicone sealer down the full lenght of it.