As with all string instruments, the strings on a piano occasionally break during tunings, especially if they undergo a lot of tightening during a pitch raise. Most notes on a piano (apart from those at the bottom of the bass end) are created by two or three strings struck simulatneously, so people sometimes choose not to replace broken strings immediately, but if they do wish to have it done, treble strings may generally be replaced on the spot, but bass strings have to be made to pattern. This means that the old string must be sent to a specialist who creates a copy with which to replace it. A treble string can be replaced for £15, whereas a replacement bass string costs £25.
Unfortunately, again, as is the case with other string instruments, new strings do not maintain their tuning for long, so you will probably notice it beginning to drift out of tune quite quickly. I can return to tune it for you, but it costs my minimum call-out fee. If you are lucky and live near to me, or we can arrange for me to pop in while I am in your area, then I shall be happy to do it for less, though, as I understand that the process of replacing a string can become deceptively expensive.
By far the most common complaint regarding a piano's general performance is that it has sticky keys (keys that return sluggishly, or not at all, once played). There are multiple reasons why a piano's keys might stick, but once the specific problem has been discovered it is usually easily repaired, and usually free of charge, unless it is present through a large proportion of the keyboard, taking a long time to fix, in which case there may be a charge.
After moving a piano to a new location, it is common practice to leave it to settle in its new situation for a while, before getting it tuned, so that it can acclimatise to the new environment (pianos are sensitive to temperature, humidity, etc.). It is beneficial to allow a piano a few weeks to settle, but if you are in a hurry then even just a few days makes a big difference..