SB800 speed light doesn't fit securely on my Nikon d610 mount shoe. Is there an adapter available or do I need to purchase a new flash?
As WayneF comments, some wiggle can be expected, and the flash should be considered secure as long as contacts are well connected (the flash does not misfire) and the flash does not come detached during normal use.
If the flash has never fit securely, it may be a manufacturing issue in which the connector was not sized to fit the camera well. (I consider any change on the camera side of the mount, as Michael Clark comments, to be included in this category.)
If it had previously fit properly, then the flash or the camera may have been damaged. More information would be needed to determine what happened.
There are various flash accessories you can use as a work around for the issue, such as voltage regulators, remote triggers, or extension cables. However, using any device that extends the length of the flash will add leverage that could result in damage to the camera or flash unit if the flash is bumped.
If you like DIY projects, you may be able to make a shim or reshape the flash connector with epoxy.