This ticket rule will take any ticket that is in an opened state for more than 7 days and move the priority to a csutom made one of "Overdue"

First you will need to have made a custom Priority state and know the ID of it in the HD_TICKET table. You can find how to do that here.

Now we will make our rule. First the select query 

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select HD_TICKET.*,
 HD_STATUS.NAME AS STATUS_NAME,
 HD_STATUS.ORDINAL as STATUS_ORDINAL,
 HD_IMPACT.ORDINAL as IMPACT_ORDINAL,
 HD_CATEGORY.ORDINAL as CATEGORY_ORDINAL,
 HD_PRIORITY.ORDINAL as PRIORITY_NUMBER,
 STATE, 
 if((datediff(DUE_DATE, now()) = 0), 2, if((datediff(DUE_DATE, now())<0), 1, 3)) as SORT_OVERDUE_STATUS,
 if(unix_timestamp(TIME_OPENED) > 0, TIME_OPENED, 1<<62) as SORT_TIME_OPENED, 
 if(unix_timestamp(TIME_STALLED) > 0, TIME_STALLED, 1<<62) as SORT_TIME_STALLED, 
 if(unix_timestamp(TIME_CLOSED) > 0, TIME_CLOSED, 1<<62) as SORT_TIME_CLOSED, 
 if(unix_timestamp(ESCALATED) > 0, ESCALATED, 1<<62) as SORT_ESCALATED,
 if(unix_timestamp(HD_TICKET.CREATED) > 0, HD_TICKET.CREATED, 1<<62) as SORT_TIME_CREATED, 
 if(unix_timestamp(HD_TICKET.MODIFIED) > 0, HD_TICKET.MODIFIED, 1<<62) as SORT_MODIFIED,
 if(unix_timestamp(HD_TICKET.DUE_DATE) > 0, HD_TICKET.DUE_DATE, 1<<62) as SORT_DUE_DATE,
 case upper(STATE) 
 when 'CLOSED' then unix_timestamp(HD_TICKET.TIME_CLOSED) - unix_timestamp(HD_TICKET.TIME_OPENED) 
 when 'OPENED' then unix_timestamp(NOW()) - unix_timestamp(HD_TICKET.TIME_OPENED) 
 else unix_timestamp(NOW()) - unix_timestamp(HD_TICKET.CREATED) end as AGE,
 if ((LENGTH(U1.FULL_NAME) = 0), U1.USER_NAME, U1.FULL_NAME) as OWNER_NAME,
 U1.FULL_NAME as OWNER_FULLNAME,
 U1.EMAIL as OWNER_EMAIL,
 if (U1.ID is null, 'z', concat('a', if ((LENGTH(U1.FULL_NAME) = 0), U1.USER_NAME, U1.FULL_NAME))) as SORT_OWNER_NAME,
 if ((LENGTH(U2.FULL_NAME) = 0), U2.USER_NAME, U2.FULL_NAME) as SUBMITTER_NAME,
 U2.FULL_NAME as SUBMITTER_FULLNAME,
 U2.EMAIL as SUBMITTER_EMAIL,
 if (U2.ID is null, 'z', concat('a', if ((LENGTH(U2.FULL_NAME) = 0), U2.USER_NAME, U2.FULL_NAME))) as SORT_SUBMITTER_NAME,
 if (U3.ID is null, 'z', concat('a', if ((LENGTH(U3.FULL_NAME) = 0), U3.USER_NAME, U3.FULL_NAME))) as SORT_APPROVER_NAME,
 if(APPROVAL='rejected', 'Rejected', if(APPROVAL='info', 'More Info Needed', if(APPROVAL='approved', 'Approved', if(APPROVER_ID>0, 'Pending', '')))) as APPROVAL_STATUS,
 Q.NAME as QUEUE_NAME 
 from (HD_TICKET, HD_PRIORITY, HD_STATUS, HD_IMPACT, HD_CATEGORY)
 LEFT JOIN USER U1 on U1.ID = HD_TICKET.OWNER_ID
 LEFT JOIN USER U2 on U2.ID = HD_TICKET.SUBMITTER_ID
 LEFT JOIN USER U3 on U3.ID = HD_TICKET.APPROVER_ID
 LEFT JOIN HD_QUEUE Q on Q.ID = HD_TICKET.HD_QUEUE_ID
 LEFT JOIN MACHINE M1 on M1.ID = HD_TICKET.MACHINE_ID
 where HD_PRIORITY.ID = HD_PRIORITY_ID
 AND HD_STATUS.ID = HD_STATUS_ID
 AND HD_IMPACT.ID = HD_IMPACT_ID
 AND HD_CATEGORY.ID = HD_CATEGORY_ID
 AND HD_TICKET.CREATED > DATE_ADD(NOW(), INTERVAL -7 DAY) 
 AND (HD_STATUS.STATE != 'closed') 
 AND HD_PRIORITY_ID != 2
 AND HD_TICKET.HD_QUEUE_ID = 1

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And the update query.

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update HD_TICKET
 set HD_TICKET.HD_PRIORITY_ID = 10
 where HD_TICKET.HD_QUEUE_ID = 1 and 
 (HD_TICKET.ID in (<TICKET_IDS>))

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Several things to note...

1. This rule is hard coded to run on the primary queue 

where HD_TICKET.HD_QUEUE_ID = 1

I like to do this with update queuries to make sure there are no unexpected surprises occuring in other queues behind the scenes. You should be extremely careful if using this on a queue other than 1 for the same reason. MAKE SURE you change the queue id before running.

2. I also hard coded the priority in 

set HD_TICKET.HD_PRIORITY_ID = 10

Make sure the id in the update query matches the one you got in the link above.

I always recommend having a test queue for testing update queries and hard coding the queue number to avoid mistakes that can cost data, time, and money, maybe even your job.

NEVER TEST A QUERY ON A LIVE QUEUE!