It sounds like you already have the setup and settings working. Properly leveling a tape recording is work in itself: the more recording time is on a vinyl record, the lower its overall volume tends to be though with newer records occasional loud passages can be accommodated by temporarily increasing track pitch.
There ought to be a "record level" dial on the tape drive.
Depending on tape material and noise reduction systems, leveling might be different. It's typical that CrO₂ tape material will be levelled at +0dB of the meters. Add +3dB when using Dolby B noise reduction. Add another +3dB for using metal tape (typically). More often than not, the peak meters will show little symbols for Dolby and possibly even for different tape material.
Usually you want to use the same level setting for all of a recording (vinyl already tends to have compressed dynamics) and the higher it is, the less the impact of tape noise/hiss will be on the recording. At the same rate, you get saturation/distortion if the setting is higher than the tape can accommodate.
Noise reduction techniques will also lead to temporary dynamic compression (moving quieter passages higher above the noise floor). There is also Dolby HX on newer tapes which reduces high frequency biasing when the signal content itself does a good enough job with that, allowing for higher level of high frequency content before saturation.
Getting that record level right is the main tape recording challenge, assuming the equipment and tapes are good.