Recently I got my bar tape, brake cables and brake levers changed, but when I picked up the bike I noticed that the brake levers were to low (at the tip of the drops) is there any way I can put them in the right position without damaging the bar tape or the brake cables?
Answer: No - you can't just move the brake levers up the curve of the handlebar drops. If you did this, the bar tape would be bunched up above the hoods and skinnied-out below the hoods.
Tools: You'll need a 5mm hex driver (maybe 4mm or 6mm, maybe a philips if its old, or flathead if its ancient) Some tape to finish the bartape wrap, and sharp scissors to cut the tape.
Method: Unwind the bar tape carefully, reposition the brakes, then do up the bar tape again. You'll probably put one, maybe two turns of bar tape below the brake hoods that were above the hoods when you started.
The brake cables should move okay - you might need to remove and refix some temporary tape.
depending on the bar tape, you may be able to undo it carefully without tearing it. Ive had success in the past. Some have very little or no adhesive. Some it takes a while for the adhesive to stick firm so if its new it may peel off just fine. Try it and see. You could also loosen the handlebar at the stem and move them up a bit to raise the hoods. This may effect cable tension for your outer cables so check that. Also you may not like having the drops angled down although some do. personal preferencesort of thing..