It depends a little on the type of Lead Acid battery you got what would be the best to do.
First thing to realise is that a 12V Lead Acid battery is not really 12V, it's between 11V and 13V, or up to 14V if gel-based when it's being used and not charged.
A normal charger will peak off at about 2.45V per cell and then let it to float-charge at about 2.3V-ish. So with a 12V battery with 6 cells that makes 14.7V peak charging voltage. That may be too much for your clock to handle, probably it'll be okay, but check that before you decide for a normal battery charger.
If you have a deep-cycle battery they like one treatment, while starter batteries (normal Motorcycle/Car batteries for example) like another.
In general, with easy to get batteries it's best to assume they are pulse or starter batteries, in which case they should be perfectly happy to exist for a decade or more being powered at a constant voltage a little below their maximum charge voltage.
So if you keep it at 13.5V (<= 2.25V per cell) it should on average be fine. You might only get 5.5Ah of capacity kept at that level, but the chance of Sulphating the battery is lower, which then statistically improves its life expectancy.
If you then have a safely current limited adapter at 13.5V that limits to about 1A, or at most 300mA above average use of your clock, your battery will never heat up significantly while it is healthy and it should stay sufficiently safe as long as there is 24hours or more between power outages (on average).
If you really want you can add a resistor in series with the battery to limit current in/out (out isn't that important):
simulate this circuit – Schematic created using CircuitLab
This way it will limit to about 500mA charge current when it's at 12.5V, 1A charge current when at 11.5V and it will slowly stop charging as it closes in on the 13.5V
Of course, when power fails your battery voltage as seen by the clock will be lowered a little due to the resistor, if the clock indeed is 400mA average use it will get 0.8V less than the battery has to offer on average.
Of course it's possible your clock uses only 50mA and 300mA-ish peak when it stamps something, you could put a capacitor parallel to your clock to pick up some slack, but that's about all the advice I can write when no further specifics are given one way or another.