Is a new DNA sample required for paternal haplotype or maternal mitochondria analysis

Can that data be used with 23&me or another testing company to have mitochondria and paternal hapalog analyzed or, is another sample needed?

What do you want to do? Please describe more precisely.

Unfortunately, different companies use different chips and different methodics for obtaining and interpreting DNA data, so there is a way to import, for example, 23andMe (or Ancestry) data into FTDNA Lab, but it is limited in features and will give you only basic information. It is also the commercial question, because FTDNA (and any other lab) wants everybody to buy it's own tests. Another idea is that there is big probability that 23andMe (or Ancestry) raw data contains Y-DNA and mtDNA data. You may extract this data on your own from your raw DNA file, but as 23andMe (or Ancestry) test is less comprehensive than FT-DNA's Y-DNA and mtDNA tests, the results will be less precise.

For example, you may use this tool: https://ytree.morleydna.com/extractFromAutosomal to extract Y-DNA info from 23andMe/Ancestry data.

I have sent your qestion to the 23andMe helpdesk and they said that they don't offer this service.

It is not possible to import genetic data from other services into a 23andMe account. Therefore you will need to purchase a kit directly from our website.

They do go on to say that

We understand that other services support this functionality

Of course they don't say which services, but if you google around for other testing companies and ask their helpdesk, you might find one that does.