Try WorldClim or the IRI Data Library

https://www.worldclim.org/

http://iridl.ldeo.columbia.edu/

Datmet data are also available, but I believe it only covers North America:

https://daac.ornl.gov/DAYMET/guides/Daymet_V3_CFMosaics.html

Hi Dear,

You may use Fick and Hijman's datasets:

Article WorldClim 2: New 1-km spatial resolution climate surfaces fo...

You may see the recent article on how they used this datasets:

Article The Grass Is Not Always Greener on the Other Side: Seasonal ...

Cheers

In addition to the earlier responses from colleagues, you could also try the ERA5 data (though not 1km resolution), but it has a fairly good spatial and temporal resolution. Here is the link

https://developers.google.com/earth-engine/datasets/catalog/ECMWF_ERA5_DAILY

In addition, these articles could also be useful

https://www.sciencedirect.com/science/article/abs/pii/S0034425717305850

https://www.sciencedirect.com/science/article/abs/pii/S0034425717305850