In general ... yes ... many accredited universities are not interested in hiring a newly-minted PhD - who hasn't yet established a promising track record showing his or her capacity to make significant contributions to the field in the near future - if the newly-minted PhD is older. The university is quietly thinking: where is the return on investment? On the other hand, if you have already begun to establish a name for yourself in your field (e.g., think Impact Factor as in publishing), and have shown the capacity to obtain funding (plenty of grant money), then you're probably going to attract interest from some universities. In short, most PhD tenure-track positions in psychology are already challenging to find, and they're even more challenging to find if you're a newly-minted older PhD who is competing for the same tenure-track positions as many other ambitious PhDs (e.g., everyone else in your cohort). Plus, many older tenured faculty are not retiring, and are continuing to work well into their 60's, 70's, or older.
Thank you.