I thought Clara's parents were dead? How come she was having Christmas lunch with them then?

Her Mother died. It was her Dad and step mother/new partner who was at dinner along with Grandma.

No. Only her mum is dead. Her dad is still alive. The younger woman was called Linda. I don't think we were told exactly who she is but I assume she is her dad's girlfriend.

I though Linda was her Aunt she seemed closer to the family than a new girlfriend,. But I don't remember being told who she was.

I must say that the actor playing her dad didn't look to me much like an older version of the young version of Clara's father that we'd already seen!

I took it as an aunt and uncle, and granny.

to be honest it came across as they thought they were showing her family for the first time as if they'd completely forgot they'd already written about the dead mother and the scenes with the younger dad