Old age in cats does not necessarily mean problems! If their body and behaviour change little by little, it is up to you to offer them a serene and peaceful transition.
While their current life expectancy varies between 15 and 18 years depending on the breed, cats are considered to be old when they are 10 years old. The weight of the passing years then begins to be felt: their physical state may change, and their behaviour may change (uncleanliness, untimely meows, disorientation, loss of balance or appetite...). Your role is to help him/her to endure these possible changes as best possible.
Adapt to their behaviour....
To do this, the key is adaptation. You must observe them and adjust your attitude according to theirs. You must continue to show your affection without forcing contact. Indeed, even the most cuddly cats can become less and less tolerant as they age. Their pains may be more severe and, even if they don't seem to be suffering, your cat may have good reasons to refuse your caresses. It is therefore better not to insist and possibly consult a veterinarian if your cat becomes too aggressive. There are also feline pheromone diffusers that help to relieve anxiety.
Of course, we should not generalise: while some cats maintain the same behaviour until the end of their lives, others, on the contrary, will see their character traits exacerbated: this is why cats who are naturally grumpy or fearful can become more and more so over the years.
... but don't be fooled!
Whatever the case, you must not leave your cat behind. Even if they are old, even sick, they need your attention. Be careful, cats are smart and can take advantage of your empathy to test boundaries... Keep in mind that if the dining room table has been forbidden for 12 years, it must remain so!
Warmth and safety
As cats age, they generally seek comfort and warmth. They appreciate the cosy corners at the bottom of a fireplace or radiator. You can offer them a comfortable blanket or cushion and cuddle them as long as they enjoy it!
Think also of the elderly: we tend to find that they do not like to see their habits changed. In cats, it's the same: their routine is comforting. The elderly cat needs stability. As much as possible, therefore, avoid moving him/her and, if you go on holiday, it is sometimes better to have them kept at home than to take them on a trip with you.
Elderly cat diet
Lastly, taking care of your elderly cat also requires an appropriate diet. Ideally, it should be enriched with antioxidants (vitamin E) and essential fatty acids. If your cat has difficulty chewing, senior cat food can be used as a substitute for kibble. You can eventually add a few treats to your cat's diet... as long as your cat is not overweight!