My 16 years old cats has a scar on the paw.

I cannot figure out how she has got it. It have been for a week. The hair seems to have fell off.

Hello - there isn't much context here to go on and despite having logged in on a proper computer, the picture still looks a bit blurred, so it's even harder than usual to tell what's going on.  For me, such lesions split into two - the painful or itchy, and the non-painful, non-itchy.  The first group includes wounds caused by trauma, for example burns, bite wounds or repetative weight-bearing on an bad surface; by itchy parasites e.g. fleas or mites; by foreign bodies e.g. grass-seeds; by self-trauma e.g. in response to pain in an underlying joint or muscle, or as a result of an allergy.  Whatever the cause, self-trauma will make it worse.   The second group includes cancers, ringworm, loss of nerve supply and viral or other systemic problems.  To make life more complex, with cats, there is a fair amount of overlap between the two groups.  e.g. Some instirnically non-itchy / non painful things can be itchy or painful for secondary reasons e.g. the area is walked on.  Some painful lesions are not licked - or certainly not in the owners' presence.  Lameness and licking can be good clues.

These amount to excellent reasons to see your vet in person; as some causes of signs like this, and some effects of signs like this, might be emergencies, it is a good idea to speak to them for triage (to establish the urgency) as soon as possible.

I took another picture. 

Thank you for this.  It does indeed look ulcerated and very sore so I think that a fairly rapid appointment, perhaps with triage (eg phone assessment) beforehand which may speed the process of getting an appointment up, is indicated.