Not directly AFAIK, but it should be not too hard to use a TriggerListener to implement such a functionality (a TriggerListener is run both a start and end of jobs, and you can set them up for individual triggers or trigger groups).
EDIT: there is even a specific FAQ Topic about this problem:
There currently is no "direct" or "free" way to chain triggers with
Quartz. However there are several ways you can accomplish it without
much effort. Below is an outline of a couple approaches:
One way is to use a listener (i.e. a TriggerListener, JobListener or
SchedulerListener) that can notice the completion of a job/trigger and
then immediately schedule a new trigger to fire. This approach can get
a bit involved, since you'll have to inform the listener which job
follows which - and you may need to worry about persistence of this
information. See the listener
org.quartz.listeners.JobChainingJobListener which ships with Quartz -
as it already has some of this functionality.
Another way is to build a Job that contains within its JobDataMap the
name of the next job to fire, and as the job completes (the last step
in its execute() method) have the job schedule the next job. Several
people are doing this and have had good luck. Most have made a base
(abstract) class that is a Job that knows how to get the job name and
group out of the JobDataMap using pre-defined keys (constants) and
contains code to schedule the identified job. This abstract Job's
implementation of execute() delegates to an abstract template method
such as "doWork()" (where the extending Job class's real work goes)
and then it contains the code for scheduling the follow-up job. Then
they simply make extensions of this class that included the work the
job should do. The usage of 'durable' jobs, or the overloaded
addJob(JobDetail, boolean, boolean) method (added in Quartz 2.2) helps
the application define all the jobs at once with their proper data,
without yet creating triggers to fire them (other than one trigger to
fire the first job in the chain).
In the future, Quartz will provide a much cleaner way to do this, but
until then, you'll have to use one of the above approaches, or think
of yet another that works better for you.