I’m sorry for your loss
First, please do check the sex of your new piggy yourself to ensure she is a sow. Pet shop missexing it happens.
It is important to note that nipping is not her being mean.
Nipping is a gesture of power and is a normal dominance behaviour. Nipping does not break the skin. She is telling the youngster that she is in charge.
(Full on bites which break the skin is not positive behaviour and means the two piggies don’t like each other.)
To bond them, you need to put them in a neutral bonding area - somewhere your older piggy does not see as her usual territory ie do not introduce them in the cage as that will be seen as a territory invasion and cause problems.
Use somewhere like a a playpen with fresh bedding added, a bathroom or kitchen floor etc.
They will need to be in the neutral bonding pen for several hours to get through the stages of bonding so make sure you can watch them and that the area is secure.
Put a pile of hay and some water in the bonding area but do not add any hides or houses (these can create territories so don’t add hides until they move back into the cage they are going to live in).
They will then go through various stages of bonding and if all goes well throughout the hours in the bonding pen (while they are still in the bonding pen) you can then thoroughly clean out and rearrange the cage they are going to live in.
After several hours in the bonding pen and if all has gone well, you can then move them into the cage and they can live together from then on. You can then add some hides now but make sure they have two exits as the piggies will still be in the bonding process for the next two weeks while they fully sort out the hierarchy and their relationship.
You will see lots of dominance - chasing, mounting, rumbling- throughout the time in the bonding pen and throughout the following weeks.
Don’t separate them if bonding has gone well. Once piggies are put together, separating them stops the bonding process and means they have to start all over again. Only separate them if the bonding clearly fails.
I'm assuming as the new piggy came from
a pet shop that she is a youngster. Youngsters are usually accepted as they can’t challenge the hierarchy but as any bond comes down to character compatibility you do need to have a plan in mind in case the bonding fails.
The guide below explains how to do a bonding
Bonding and Interaction: Illustrated social behaviours and bonding dynamics
Some further guides which you may find useful
Sows: Behaviour and female health problems (including ovarian cysts)
Dominance Behaviours In Guinea Pigs
A - Z of Guinea Pig Behaviours
these are my daughters pets so I went and purchased a baby girl today to heal their and the other pigs sadness. I keep trying to introduce them to each other but the older female is being mean 
she’ll sniff and lick a little bit but then goes to nipping at her. How do I go about handling this? I’m not sure if this has something to do with her “sister” missing or what.
