The moving celestial poles drag the whole celestial-coordinate system — the whole grid of declination and right ascension — along with them. ... Because the coordinate grid insists on sliding around this way, a star's right ascension and declination are continually changing.

How does right ascension change over time?

Right ascension for "fixed stars" near the ecliptic and equator increases by about 3.05 seconds per year on average, or 5.1 minutes per century, but for fixed stars further from the ecliptic the rate of change can be anything from negative infinity to positive infinity.

Does the right ascension and declination of a star change during the night?

Right Ascension (or "RA") and Declination (or "Dec") are global coordinates: any particular star has the same RA and Dec for all observers on Earth, and that position remains the same, night after night.