Citing a piece in the form "Author et al" if main citation style is "numeric"

If you can switch from the IEEEtran to the IEEEtranN bibliography style (the N in IEEEtranN stands for natbib), you can make use of natbib's citeauthor and citet macros to generate citation call-outs in the desired format.

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Addendum to address the OP's requirement that the string "et al." must be typeset in italics:

I suggest you proceed as follows to achieve this objective:

• Find the file IEEEtranN.bst in your TeX distribution. Make a copy of this file and call the copy, say, IEEEtranN-ital.bst. (Do not edit an original file of the TeX distribution directly.)

• Open the file IEEEtranN-ital.bst in a text editor. The program you use to edit your tex files will do fine.

• In the file IEEEtranN-ital.bst, find the following line (l. 201 in my copy of the file):

  FUNCTION {bbl.etal}{ "et~al." }
  

  Change it to

  FUNCTION {bbl.etal}{ "textit{et~al.}" }
  

• Save the file IEEEtranN-ital.bst, either in the directory that contains your main tex file or in a directory that's searched by BibTeX. If you select the latter option, be sure to update the filename database of your TeX distribution suitably.

• In your main tex file, change the instruction

  bibliographystyle{IEEEtran}
  

  to

  bibliographystyle{IEEEtranN-ital}
  

  and run a full recompile cycle: LaTeX, BibTeX, and LaTeX twice more. Then, start using the citeauthor and citet instruction as and where needed. (I assume that, so far, your document contains only cite instructions. Please advise if this is not the case.)

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The following MWE (minimum working example) loads the hyperref package purely to highlight what's generated by cite, citeauthor, and citet.

documentclass{IEEEtran}

begin{filecontents}[overwrite]{mybibfile.bib}
@misc{jones,
  author  = "Dorothy Jones and Daniela Smith and Dinah Webster",
  title   = "Thoughts",
  year    = 3001,
}
end{filecontents}

usepackage[numbers]{natbib} % 'natbib' is a citation management package
bibliographystyle{IEEEtranN-ital}

usepackage[colorlinks,allcolors=blue]{hyperref} % optional

begin{document}
cite{jones} % standard numeric-style citation call-out

In cite{jones}, citeauthor{jones} studied dots

dots some phrases citet{jones} studied dots % author-number citation call-out

bibliography{mybibfile}
end{document}