Assuming, as you say, that the process is gradual enough to avoid overt damage to the planet …
The change is about 4% (1/24). Not huge, but enough to be above the noise floor of any delicately balanced system.
In terms of pure physics, the days & nights will both be longer. This ought to lead to greater diurnal temperature variation. That could drive more fog in areas prone to fog, and more and harder freezes earlier in the fall.
On a biological level, it could mess up many animals who’s behavior is strongly circadian-driven. Plants in areas with little seasonal variation, e.g. those growing below about 30 degrees latitude, may have more trouble with the creater diurnal variation.
On the scienctific level, we would need to add some conversion factors to metrology & astronomy, but they already deal with the fact the Earth rotational day is neither constant, nor 24.0000000… hours long.
On a gross human society level, we’d have a lot of rejiggering to do. Do we stick with a 40 hour work week and everybody gets an extra hour off? Or do we work 9 instead of 8? Or do we decide the simplest way is to redefine the size of an “hour” so there are 24 of them in the new rotational period?
Lotsa confusion & wrangling, but not much else.